Neutrosophic Fuzzy Ideal Open Sets, Ideal Closed Sets, and Their Applications in Geographic Information Systems

نوع المستند : المقالة الأصلية


1 Math and Computer Science, Faculty of Science, Port Said University, Egypt

2 Dept. of Mathematics and Basic sciences, Ministry of Higher Education, Higher Future institute of Engineering and Technology in Mansour, Egypt


The paper explores the concepts of neutrosophic fuzzy ideal open sets and neutrosophic fuzzy ideal closed sets in neutrosophic fuzzy spaces. It establishes their properties and relationships with other neutrosophic fuzzy topological concepts. The authors also introduce NPL-closed sets, which generalize the concept of NPL-open sets due to Abd El-Monsef et al [1, 2]. They define and study two types of neutrosophic fuzzy pairwise functions: neutrosophic fuzzy pairwise preopen functions and neutrosophic fuzzy pairwise preclosed functions. These concepts provide a deeper understanding of the topological structure and relationships between neutrosophic fuzzy spaces. Additionally, the paper highlights the practical applications of this research in Geographic Information Systems (GIS), such as representing uncertainty in spatial data caused by factors like measurement errors, sensor limitations, and data incompleteness using neutrosophic fuzzy sets. This application is useful for tasks such as land use classification, disease outbreak analysis, urban planning, forest fire spread monitoring, and wildfire risk assessment. The research also enables spatial pattern analysis and recognition while considering inherent uncertainty, decision-making in spatial planning by representing uncertain or indeterminate decision criteria, spatiotemporal analysis of uncertain data while monitoring forest fires in remote areas with limited sensors and communication infrastructure, and risk assessment and disaster management by representing uncertainty in risk factors and hazard models for natural disasters and other hazards. These applications have broad potential for further development and innovation in GIS.

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